Extra dimensions

Origins...

Kaluza (1921) and Klein (1926) proposed an extra spacial dimension trying to unify EM with Gravity:

"Long live the fifth dimension" Einstein's letter to Ehrenfest 21/1/1928

hMN = (hµν , h5µ, h55)M = µ, 5 = 1, 2, 3, 4, 5

1926 using a formalism that is usually called Kaluza-Klein reduction [5]. Although their initial

motivation and ideas do not seem to be viable, the formalism that they and others developed

is still useful nowadays. This is the one that will be considered below.

y

xµ

Figure 1 Compactification on S1

For simplicity, we will start with a 5D field theory of scalars. The action is given by

S5 = !!

d4x dy M!

"

|!µ"|2 + |!y"|2 + g25|"|4

#

, (4)

where by y we refer the extra fifth dimension. We have extracted a universal scale M! in front

of the action in order to keep all the 5D fields with the same mass-dimension as in 4D. Let

us now consider that the fifth dimension is compact and flat. We will consider that it has the

topology of a circle S1 as Fig. 1. This corresponds to the identification of y with y + 2#R. In

such a case, we can expand the 5D complex scalar fields in Fourier series:

"(x, y) ="

$

n=#"

einy/R"(n)(x) = "(0)(x) +$

n $=0

einy/R"(n)(x) , (5)

that inserted in Eq. (4) and integrated over y gives

S5 = S(0)4 + S(n)

4 (6)

4

x₅In 5 dimensions the gravitational field

has more components:

4 dimensional gravit. field4 dimensional EM field

The extra spacial-dimension had to be compactified

R

R~1/MP Einstein liked the idea:

... but didn’t work: Not possible to incorporate matter

symmetric under M ↔ N

The formalism developed however was useful:For periodic extra dim., one can perform a Fourier expansion of 5D fields:

5D field = 4D massless state (n=0) + infinity tower of 4D massive states

Kaluza-Klein states

QM

States with 5D momentum ~ mass in 4D:

1/R2/R3/R

MASS

0

eip5x5 p5 = n/R

...equivalent of harmonics

p2µ = p2

5

,

Φ(x, x5) =∞�

n=−∞einx5/R Φ(n)(x)

● The next incarnation of extra dimensions came around 1980, when string theory was developed as a theory of quantum gravity.

● It was shown that string theory could only be made consistent if the spacetime dimensions were larger than four.The extra dimensions were supposed to be compactified close to the Planck scale:

radius ~ 1/MP

Therefore not testable in near-future experiments

In 1998 Arkani-Hamed, Dimopoulos and Dvali (ADD) realize that extra dimensions could explain the weakness of gravity:

GN << GF

How? Gauss’s law:V ∼ Qint

r

V ∼ Qint

r1+d

d = number of extra dimensions

4 dim

4+d dim

At large distances, the strength of a force becomes smaller in higher dimensions

�

SdΦ ∼ Qint

S ∼ r2+d

BUT:

1) Only gravity could propagate in these extra dimensions

(otherwise all forces will be weak)

d extra dimensions

SM particles

Gravity

4D

Possible in “Brane Worlds” (String constructions):

2) We see at large distances only 3 spacial dimensions, so these extra dimensions have to be compactified.

How large can they be?Surprisingly, we have not measured very well gravity at

distances smaller ~ 0.1 mm

Figure 5: Present limits on new short-range forces (yellow regions), as a function oftheir range ! and their strength relative to gravity ". The limits are compared to newforces mediated by the graviton in the case of two large extra dimensions, and by theradion.

(transverse) volume limit and is expected to acquire a small mass suppressedby the volume, of order (8). In the standard realization, its coupling to matteris given via the energy momentum tensor [31], while in general there are moreterms invariant under non-linear supersymmetry that have been classified, upto dimension eight [32, 33].

An explicit computation was performed for a generic intersection of twobrane stacks, leading to three irreducible couplings, besides the standard one [33]:two of dimension six involving the goldstino, a matter fermion and a scalar orgauge field, and one four-fermion operator of dimension eight. Their strengthis set by the goldstino decay constant !, up to model-independent numericalcoe!cients which are independent of the brane angles. Obviously, at low en-ergies the dominant operators are those of dimension six. In the minimal caseof (non-supersymmetric) SM, only one of these two operators may exist, thatcouples the goldstino " with the Higgs H and a lepton doublet L:

Lint! = 2!(DµH)(LDµ") + h.c. , (11)

where the goldstino decay constant is given by the total brane tension

1

2 !2= N1 T1 + N2 T2 ; Ti =

M4s

4#2g2i

, (12)

13

3.1.1 Measuring the gravitational force at millimeter distances

The KK of the graviton give rise to new forces. Since they are massive particles they produce

a Yukawa-type force. For the first KK (n1 = ±1, n2 = 0 and n1 = 0, n2 = ±1) of masses 1/R,

this force is given by

FKK(r) = !!GNm1m2

re!r/! , (24)

where ! = 4 for a 2-torus compactification 3 and " = R. Searches for new forces has been

carried in several experiments. Nevertheless, the bounds on ! are very weak at distances r

below a millimeter. In Fig. 2 we plot the present experimental bounds on ! and ". The latest

experiment, based in a torsion pendulum Fig. 3, has excluded the region R " 0.2 mm [10].

3.1.2 Collider experiments

It is easy to estimate that the contributions of the KK gravitons to any physical process

measured in any collider are small. For example, let us consider the process BR(K # # +

gravitons). We can use Eq. (22) with E $ mK and obtain

BR(K # # + gravitons) $!

mK

M"

"4

$ 10!12 , (25)

for M" $ TeV. This is close to the experimental constraint but it does not ruled out the model.

Similarly, we can estimate the contribution of the KK-tower of gravitons to other low-energy

processes:

BR(J/! # $ + gravitons) $!

mJ/!

M"

"4

$ 10!10 ,

BR(Z # f f + gravitons) $!

mZ

M"

"4

$ 10!4 . (26)

None of them contradict the experimental bounds. Up to date, no collider experiment has been

able to exclude this scenario. The present limit from colliders arises from the process

e+e! # $ + gravitons , (27)

3For a 2-sphere compactification we have ! = 3.

10

Constrains on extra forces:

α = measures the strength of the interaction (α=1 ! Gravit. strength)

λ = range of the interaction

Gravity coud be different at sub-mm scales: Extra dim of radius R~0.04 mm

possible!

ADD proposed the following scenario:

EW scale

Cutoff of the SM ~ Λ ~ Mstring:

Gravity strength :

~ TeV

~ 100 GeV

dilution factor due to the spreading of the gravitational field lines

in d extra dimensions

Scale at which gravity is strong

2) Gravity propagating in d extra dimensions of size R:

Since MW ~ Λ ~ Mstring, no big hierarchy problem!

GN =1

M2P

∼ 1M2

string

1(Mstring2πR)d

1)

d=1 ! R ~10! Km d=2! R ~ 0.1 mm

... d=6 ! R ~ 1/ MeV

Mstring ~ TeV

GN =1

M2P

∼ 1M2

string

1(Mstring2πR)d

Not possible

~ at the verge of the exp. bounds

OK

Predictions:

“The only prediction of string theory is that there are no predictions”

Anonymous

1) The space must be1+9 dimensional2) There are string excitations of higher-energy

2) String theory at the reach of the LHC

But we already said...

No clear predictions on what to expect!

The only generic ones:

1) For d=2, we expect deviations from Newtonian gravity at distances smaller than ~ 0.1mm

The 1st KK-graviton of mass ~1/(0.1mm) give a “new” interaction (a “new” force)

Model-independent signals from gravity at ~TeV:

Gravity becomes strong at ~ TeV energies:

KK-Gravitons

GN =1

M2P

�

n

Sum over all KK-gravitons

�

n

GNQ2 ∼ 1M2

string

Q2~

arXiv:hep-ex/0310020v1

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To appear in : Proceedings of the International Europhysics Conference on High Energy PhysicsEPS 2003, Aachen, GermanySession: String theory and extra dimensions

Search for Extra Dimensions at LHC

Laurent Vacavant, for the ATLAS and CMS Collaborations

Lawrence Berkeley National Laboratory, Physics Division, Berkeley CA 94720, USA

Received: February 7, 2008

Abstract. Some of the studies performed by the ATLAS and CMS collaborations to establish the futuresensitivity of the experiments to extra dimension signals are reviewed. The discrimination of those signalsfrom other new physics signals and the extraction of the underlying parameters of the extra dimensionmodels are discussed.

1 Introduction

Models with extra dimensions (ED) (see [1]) are very at-tractive extensions of the Standard Model (SM), in partic-ular with respect to the hierarchy problem. While ED haveso far escaped detection [2], they could manifest them-selves at LHC via a rich and varied phenomenology.

This review focuses on the three main classes of EDmodels with prediction at the TeV scale. The aim of thestudies was two-fold: establishing the sensitivity to ED sig-nals using detector simulation and various physics back-grounds, as well as assessing whether enough informationcould be extracted in order to distinguish ED signaturesfrom other new physics signals.

The studies are based on fast simulation tools whichdescribe accurately the expected detector performance.The relevant aspects of the simulation have been vali-dated [3] in full simulation and with test-beam data when-ever possible. Except when stated otherwise, all the resultsand plots presented here are for an integrated luminosityof 100 fb!1 collected by one of the experiments (i.e. oneyear at the nominal luminosity of LHC, 1034 cm!2s!1).

2 Large Extra Dimensions

In this scenario, the SM fields are confined in our 4D worldand only gravity propagates in the bulk. The model ischaracterized by the number of extra dimensions ! and bythe new fundamental scale MD. The graviton expands in4D into a tower of Kaluza-Klein (KK) excitations whichcouple universally to all SM fields. Even though this cou-pling is small (1/MPl), the large number of states andtheir small mass splitting lead to sizeable cross-sectionsat the LHC.

The virtual exchange of KK excitations of graviton canlead to deviations in Drell-Yan cross-sections and asymme-tries in SM processes. The left plot of Fig. 1 illustrates suchdeviations in the "" invariant mass distribution [4]. Thiskind of signatures is clear, very sensitive to new physics

1

10

10 2

10 3

10 4

10 5

10 6

0 250 500 750 1000 1250 1500 1750 2000

jW(e!), jW(µ!)

jW("!)

jZ(!!)

total background

signal #=2 MD = 4 TeVsignal #=2 MD = 8 TeVsignal #=3 MD = 5 TeVsignal #=4 MD = 5 TeV

$s = 14 TeV

ETmiss (GeV)

Even

ts /

20 G

eV

Fig. 1. Large ED. Left plot [4]: virtual exchange of gravitons.The plot shows the deviation in Drell-Yan cross-section pp !

!! (top curve) with respect to the SM expectation [4]. Rightplot [5]: direct production. Missing energy distribution (dots),shown here for various choices of the number of ED (") and ofthe mass scale (MD) and for SM backgrounds (histograms).

and could signal the existence of extra dimensions. How-ever the underlying parameters of the model cannot beextracted in this case because the model is sensitive tounknown ultra-violet physics.

The second class of signatures is the direct productionof KK excitations of graviton which will escape detectionin 4D: qq ! gG(k), gq ! qG(k) and gg ! gG(k). In thiscase, the main signature to look for is some missing energyaccompanied by a mono-jet (Fig. 1, right plot) [5]. Withinthe allowed region for the e!ective theory (

"s < MD),

those processes can be reliably calculated and the param-eters of the model can be constrained from the measure-ments. Models with up to four extra dimensions could beprobed at LHC. For 100 fb!1, the maximum reach in MD

is between 9.1 TeV (! = 2) and 6.0 TeV (! = 4), cor-responding to a radius of compactification between 8 µmand 1 pm. The two parameters of the model can in prin-ciple be extracted from the absolute cross-section of theprocesses or more definitely by collecting # 50 fb!1 ofdata at a di!erent center-of-mass energy.

To be seen at LHC as deviations in Drell-Yan cross-sections for SM processes.

Example: deviations in the γγ invariant mass distribution of pp"γγ:

KK-Graviton production:

Search for:Mono-jet + Missing energy

arX

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1002

0v1

10

Oct

200

3

To appear in : Proceedings of the International Europhysics Conference on High Energy PhysicsEPS 2003, Aachen, GermanySession: String theory and extra dimensions

Search for Extra Dimensions at LHC

Laurent Vacavant, for the ATLAS and CMS Collaborations

Lawrence Berkeley National Laboratory, Physics Division, Berkeley CA 94720, USA

Received: February 7, 2008

Abstract. Some of the studies performed by the ATLAS and CMS collaborations to establish the futuresensitivity of the experiments to extra dimension signals are reviewed. The discrimination of those signalsfrom other new physics signals and the extraction of the underlying parameters of the extra dimensionmodels are discussed.

1 Introduction

Models with extra dimensions (ED) (see [1]) are very at-tractive extensions of the Standard Model (SM), in partic-ular with respect to the hierarchy problem. While ED haveso far escaped detection [2], they could manifest them-selves at LHC via a rich and varied phenomenology.

This review focuses on the three main classes of EDmodels with prediction at the TeV scale. The aim of thestudies was two-fold: establishing the sensitivity to ED sig-nals using detector simulation and various physics back-grounds, as well as assessing whether enough informationcould be extracted in order to distinguish ED signaturesfrom other new physics signals.

The studies are based on fast simulation tools whichdescribe accurately the expected detector performance.The relevant aspects of the simulation have been vali-dated [3] in full simulation and with test-beam data when-ever possible. Except when stated otherwise, all the resultsand plots presented here are for an integrated luminosityof 100 fb!1 collected by one of the experiments (i.e. oneyear at the nominal luminosity of LHC, 1034 cm!2s!1).

2 Large Extra Dimensions

In this scenario, the SM fields are confined in our 4D worldand only gravity propagates in the bulk. The model ischaracterized by the number of extra dimensions ! and bythe new fundamental scale MD. The graviton expands in4D into a tower of Kaluza-Klein (KK) excitations whichcouple universally to all SM fields. Even though this cou-pling is small (1/MPl), the large number of states andtheir small mass splitting lead to sizeable cross-sectionsat the LHC.

The virtual exchange of KK excitations of graviton canlead to deviations in Drell-Yan cross-sections and asymme-tries in SM processes. The left plot of Fig. 1 illustrates suchdeviations in the "" invariant mass distribution [4]. Thiskind of signatures is clear, very sensitive to new physics

1

10

10 2

10 3

10 4

10 5

10 6

0 250 500 750 1000 1250 1500 1750 2000

jW(e!), jW(µ!)

jW("!)

jZ(!!)

total background

signal #=2 MD = 4 TeVsignal #=2 MD = 8 TeVsignal #=3 MD = 5 TeVsignal #=4 MD = 5 TeV

$s = 14 TeV

ETmiss (GeV)

Even

ts /

20 G

eV

Fig. 1. Large ED. Left plot [4]: virtual exchange of gravitons.The plot shows the deviation in Drell-Yan cross-section pp !

!! (top curve) with respect to the SM expectation [4]. Rightplot [5]: direct production. Missing energy distribution (dots),shown here for various choices of the number of ED (") and ofthe mass scale (MD) and for SM backgrounds (histograms).

and could signal the existence of extra dimensions. How-ever the underlying parameters of the model cannot beextracted in this case because the model is sensitive tounknown ultra-violet physics.

The second class of signatures is the direct productionof KK excitations of graviton which will escape detectionin 4D: qq ! gG(k), gq ! qG(k) and gg ! gG(k). In thiscase, the main signature to look for is some missing energyaccompanied by a mono-jet (Fig. 1, right plot) [5]. Withinthe allowed region for the e!ective theory (

"s < MD),

those processes can be reliably calculated and the param-eters of the model can be constrained from the measure-ments. Models with up to four extra dimensions could beprobed at LHC. For 100 fb!1, the maximum reach in MD

is between 9.1 TeV (! = 2) and 6.0 TeV (! = 4), cor-responding to a radius of compactification between 8 µmand 1 pm. The two parameters of the model can in prin-ciple be extracted from the absolute cross-section of theprocesses or more definitely by collecting # 50 fb!1 ofdata at a di!erent center-of-mass energy.

arXiv:hep-ex/0310020v1

Gauge theories in a slice of AdS5

Extra Dim

4 Dim

Extra Dim

4 Dim

Alex Pomarol, CERN

z

In 1999 Randall and Sundrum had a different idea:

ds2 = a(z)2[dx

2 + dz2]

Anti-de-Sitter (AdS):

a =

L

zHere the observer sees

that the atomic transition is less

energetic

Use gravitational redshift factors to explain the difference between MP and the EW-scale

Assume that the extra-dimensional geometry is non-flat Scales shrink as we move in the extra dimension

Qualitatively can be understood as the photon loosing kinetic energy as it climbs up the gravitational potential well:

E1

E2

E2 < E1

Earth

Gauge

theorie

sin

aslic

eofAdS

5

Extra

Dim

4Dim

Extra

Dim

4Dim

Alex

Pom

aro

l,CERN

Similarly...

Placing the Higgs in the interior of the extra dimension could explain why its mass-term is smaller than MP:

In this boundary the scales

can be very large ~MP

Randall-Sundrum IdeaGauge theories in a slice of AdS5

Extra Dim

4 Dim

Extra Dim

4 Dim

Alex Pomarol, CERN

z

ds2 = a(z)2[dx

2 + dz2]

Anti-de-Sitter (AdS):

a =

L

z

Higgs

In this boundary the scales

are smaller ~MW

Two scale model

Alternative understanding by looking at the wave-function of a graviton in a AdS-space

.

.

Higgs!

M5D > k/2

UV-bound. IR-bound.

The small SM fermion masses originate from small

wave-function overlapping. GIM-like mechanism T.Gherghetta, A.P.

Graviton

As in QM: Small overlapping of wave-functions = small couplings # gravity is weak for the Higgs!!

In 1999 when Sundrum was explaining this idea in a conference in Santa Barbara, E. Witten stood up and more or less said:

“This is as having a composite Higgs made of strongly-coupled fields of a conformal field theory (CFT)”

What did he have in mind? The AdS/CFT correspondence:

Maldacena 97

Strongly coupled 4D

theories in certain limits

duality Weakly coupled

gravity theories in

higher-dimensions

Composite states have similar dynamics as particles in a curved extra dimension $ Holography: ”4D composite states

encode 5D information”

One can check certain things for a Higgs in an AdS-extra dimension:

The form factor of a 5D Higgs follows

the expectation for a composite state

Composite state

p

Electromagnetic form factor of

the pion F!(p)

Coupling of the pion to the external photon

! ! !

"

! !

"

#(n)

"F!(p) =

!

n gVn!!MVnFVn

p2+M2Vn

a) At p = 0:

Charge normalization F!(0) = 1 ! g#!!F# # M#

$$ F# #%

3F!b) Large momentum:

Conformal symmetry says F! $ 1/p2

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

F!(p)

p [GeV]

Similar to VMD (dashed line): F!(p) =M 2

#

p2+M 2#

successful exp.!!

hh

Fh(p)

Fh(p) W

W

● KK of W

Example:

Five Dimensional composite Higgs model.

Minimal 5D composite Higgs model

AdS5

SO(5)! U(1)

Fermions " 5 of SO(5)

UV-bound.

SU(2)L! U(1)Y

IR-bound.

SO(4)! U(1)

Parameters: g5D, L and 5D fermion masses Agashe, A.P.,Contino

Gravity + SM gauge bosons SU(3) x SU(2) x U(1)+ SM fermions

Text HIGGS

TeV-scalesMP-scales

Nice “geometrical” explanation of the smallness of some of the SM fermion masses

Small masses for fermions (e.g. electron) easy to generate by having the wave-functions picked towards the opposite

boundary to the Higgs

.

.

Higgs!

M5D > k/2

UV-bound. IR-bound.

The small SM fermion masses originate from small

wave-function overlapping. GIM-like mechanism T.Gherghetta, A.P.

Electron

Spectrum

500-1500 GeV

2.5 TeV

Higgs

gauge KK

top fermionic KK

4.2 TeV graviton KK

the higher the spin, the higher the mass

Unknown value

.

Minimal 5D composite Higgs model

AdS5

SO(5)! U(1)

Fermions " 5 of SO(5)

UV-bound.

SU(2)L! U(1)Y

IR-bound.

SO(4)! U(1)

Parameters: g5D, L and 5D fermion masses Agashe, A.P.,Contino

extra dim

The bosonic sector:

Five Dimensional composite (PGB) Higgs model

Why this symmetry breaking pattern?

We are in 5D: AM = (Aµ,A5)

Massless boson spectrum:

• Aµ of SU(2)L!U(1)Y = SM Gauge bosons

• A5 of SO(5)/SO(4) = 2 of SU(2)L = SM Higgs

!" Higgs-gauge unification

Higgs mass protected by 5D gauge invariance!

Hosotani mechanism

A5 ! A5 + !5"

shifts as a PGB

Predictions

Light Higgs KK resonancesfor each SM field

in complete reps of the bulk group SO(5)

+

top: 5 = 27/6 + 21/6 + 12/3

exotic states of Q=5/3

Spectrum

110-180 GeV

500-1500 GeV

2.5 TeV

Higgs

12/3

gauge KK

color fermionic KK}21/6

27/6

4.2 TeV graviton KK

the higher the spin, the higher the mass

How to see the KK at Hadron Colliders?(and similarities/distinction with other models)

Higgsless Composite/PGB Higgs

TC 5D models 5D HiggsLittle Higgs

W !, Z !

Higgsless Composite/PGB Higgs

TC 5D models 5D HiggsLittle Higgs

W !, Z !! leptons

W !, Z !! tops, Wlong, Zlong, h

W !, Z !

Decay:

Possible to see up to 2 TeV

Higgsless Composite/PGB Higgs

TC 5D models 5D HiggsLittle Higgs

g! ! tt

g!

Decay:

6

TABLE I: Selection cuts in the semileptonic tt channel.

3. Di!erential cross section

The SM top pair production rate falls steeply as a func-tion of the invariant mass. The uncertainty from PDF’sin this shape is far less than that in the total cross-section.Hence we look for a signal from KK gluons in the di!er-ential tt cross-section as opposed to simply counting thetotal number of tt events. We do not expect a sharpresonance in this distribution due to the large width ofthe KK gluon, but we do obtain a statistically significant“bump” as discussed below.

The di!erential cross section as a function of mtt isshown in Figs. 4 and 5 for MKKG = 3 TeV producedat the LHC. In Fig. 4 we compare the total (signal +background) distribution to the SM (background) distri-bution, based on a partonic-level analysis. In Fig. 5, wefocus on the area near the peak and we consider con-tributions from the reducible background (from Wjj).We show the particle level results and the correspond-ing statistical uncertainties of event reconstruction. Thepredictions for the SM and SM+RS models, based onpartonic-level analysis (same as in Fig. 4), are also shownfor comparison. We see that, since the partonic and par-ticle level data are consistent with each other, we do notexpect a large bias in the ability to reconstruct the KKGmass.

/ GeVtt

m1000 1500 2000 2500 3000 3500

# o

f even

ts / 2

00 G

eV

210

310

410 jj)!lbb"tt"(pptt

dm#d

-1Ldt = 100 fb$

Signal + Background

Background

FIG. 4: Invariant tt mass distribution for MKKG = 3 TeVproduction at the LHC. The solid curve presents sig-nal+background distribution, while the dashed curve presentsthe tt SM background, based on partonic level analysis.

In the following we describe the reconstruction e"-ciency and how we estimate our signal to backgroundratio and the sensitivity to the KK gluon mass based onthis analysis. Following [13], we assume a 20% e"ciency

invariant mass / GeVtt

2000 2500 3000 3500 4000

-1# e

ven

ts / 2

00 G

eV

/ 1

00 f

b

0

10

20

30

40

50

60 mass distributiontt

total reconstructed

total partonic

W+jets background

SM prediction

FIG. 5: Invariant tt mass distribution for 3 TeV KKG, fo-cusing on the area near the peak. The error bars corre-spond to statistical uncertainties and represent our particlelevel analysis. The dotted line stands for the SM predic-tion. The dashed-dotted line shows the Wjj background.The dashed line shows the signal+background from Sherpa’spartonic level analysis.

for tagging b-jets (!b), independent of the b-jet energy.Our particle level study shows that the e"ciency of theadditional cuts described, !cut, in Table I for the recon-struction of tt system in the mass window around KKGis about 20(21)% for mtt = 3(4)TeV. We find that forthe SM the reconstruction e"ciency is lower, 9(10)% formtt = 3(4) TeV. The signal+background (BG+KKG)and background (BG) reconstruction e"ciencies di!erbecause the BG and BG+KKG events have di!erentkinematics. The background is dominated by gg fusionevents which are more forwardly-peaked in the top paircenter of mass (cm) frame than the qq fusion events.Hence, the gg events have a smaller PT

9 than the qqevents. Since KK gluon signal comes only from qq fu-sion, the pT cut on the top-quark reduces backgroundmore than the signal.

In addition, the branching ratio for the lj decay is givenby BRlj = 2 ! 2/9 ! 2/3 " 0.3. The total e"ciency isgiven by BRlj ! !cut ! !b # 1%.

We estimate the statistical significance of our signalby looking at the bump. An invariant tt mass windowcut 0.85MKKG < Mtt < 1.5MKKG is applied. Thelower bound corresponds roughly to the width. Theupper bound is not particularly important due to thesteep fallo! in cross section. Below the MKKG thresh-old, the signal+background distribution is actually be-low the background one due to destructive interference.Therefore, we choose an asymmetric mass window cut.We estimate the ratio of the signal, S, to the statisticalerror in the the background,

$B, via our particle level

9 Note that, inside the mass window, the total momentum/energyof each top quark in cm frame is roughly fixed at MKKG/2.

Agashe et al

Possible up to 4 TeV

Higgsless Composite/PGB Higgs

TC 5D models 5D HiggsLittle Higgs

feasible to see up to 1-2 TeV

t!

R

t!

R ! WlongbDecay:

Higgsless Composite/PGB Higgs

TC 5D models Little Higgs

feasible to see up to 1-2 TeV

Decay:

5D Higgs

T5/3

T5/3 ! Wlongt

q q!

g

g

T5/3

q!

q

g

W"

W+ b

b

t

l+ !l+ !

tT5/3

W"

W+

l+ q!

g

g

B

!

q

g

W"

W+ b

b

t

q q! l+ !

t

B

W+

W"

Figure 1: Pair production of T5/3 and B to same-sign dilepton final states.

(section 4). Sections 5 and 6 present our main analysis: first, we show the optimal cuts andcharacterize the best observables for discovering the heavy T5/3 and B without making anysophisticated reconstruction; then, we reconstruct the W and t candidates and pair them toreconstruct the T5/3 invariant mass. We conclude with a critical discussion of our results.

2 A simple model for the top partners

Although the main results of our analysis will be largely independent of the specific real-ization of the new sector, we will adopt as a working example the “two-site” description ofRef. [23], which reproduces the low-energy regime of the 5D models of [13, 14] (see also [24]for an alternative 4D construction). Its two building blocks are the weakly-coupled sec-tor of the elementary fields qL = (tL, bL) and tR, and a composite sector comprising twoheavy multiplets (2, 2)2/3, (1, 1)2/3 plus the Higgs (the case with partners of the tR in a[(1, 3) # (3, 1)]2/3 can be similarly worked out):

Q = (2, 2)2/3 =

!

T T5/3

B T2/3

"

, T = (1, 1)2/3 , H = (2, 2)0 =

!

!†0 !+

"!! !0

"

. (1)

The two sectors are linearly coupled through mass mixing terms, resulting in SM and heavymass eigenstates that are admixtures of elementary and composite modes. The Higgs dou-blet couples only to the composite fermions, and its Yukawa interactions to the SM andheavy eigenstates arise only via their composite component. The Lagrangian in the elemen-tary/composite basis is (we omit the Higgs potential and kinetic terms and we assume, forsimplicity, the same Yukawa coupling for both left and right composite chiralities):

L =qL $" qL + tR $" tR

+ Tr#

Q ( $" " MQ)Q$

+ ¯T ( $" " MT ) T + Y" Tr{QH} T + h.c

+ !L qL (T, B) + !R tRT + h.c.

(2)

3

If this fermion is light, it can be double produced:

Contino,Servant,see also Saavedra, !Wulzer, Disertori

masses up to 1 TeV reached with an integrated luminosity of 20/fb

two like-sign leptons